Given the function g(x) = 4(3)x, section a is from x = 1 to x = 2 and section b is from x = 3 to x = 4.

a) find the average rate of change of each section. (4 points)

Easy peasy

the average rate of change in section A is the slope from (1,g(1)) to (2,g(2))
the average rate of chagne in section B is the slope from (3,g(3)) to (4,g(4))

A.

section A
g(1)=4(3)^1=12
g(2)=4(3)^2=4(9)=36
slope=(36-12)/(2-1)=24/1=24

section B
g(3)=4(3)^3=4(27)=108
g(4)=4(3)^4=4(81)=324
slope=(324-108)/(4-3)=216/1=216

section A has an average rate of change of 24
section B has an average rate of change of 216